$A$ pump on the ground floor of a building can pump up water to fill a tank of volume $30 \; m^{3}$ in $15 \; min$. If the tank is $40 \; m$ above the ground, and the efficiency of the pump is $30 \%$, how much electric power (in $kW$) is consumed by the pump?

$A$ truck of mass $10,000 \ kg$ is moving up an inclined plane with a slope of $1 \ m$ in $50 \ m$. If the speed of the truck is $36 \ km/hr$,find the power of the engine in $kW$. (Take $g = 10 \ m/s^2$)

An elevator can carry a maximum load of $1800 \; kg$ (elevator $+$ passengers) and is moving up with a constant speed of $2 \; m s^{-1}$. The frictional force opposing the motion is $4000 \; N$. Determine the minimum power delivered by the motor to the elevator in watts as well as in horsepower.

At any instant of time $t$, the displacement of a particle is given by $x = 2t - 1$ ($SI$ units) under the influence of a force of $5 \,N$. The value of instantaneous power is (in $SI$ units):

The ratio of powers of two motors is $\frac{3 \sqrt{x}}{\sqrt{x}+1}$,which are capable of raising $300 \ kg$ of water in $5 \ minutes$ and $50 \ kg$ of water in $2 \ minutes$ respectively from a well of $100 \ m$ depth. The value of $x$ is:

$A$ force of $(60 \hat{i} + 15 \hat{j} - 3 \hat{k}) \text{ N}$ produces a velocity of $(2 \hat{i} - 4 \hat{j} + 5 \hat{k}) \text{ m/s}$ in a particle. The value of power at that time will be: (in $\text{ W}$)